85727 - Applied Signal Processing M

Course Unit Page

Academic Year 2020/2021

Learning outcomes

The course aims at reviewing basic concepts of probability, operator theory and optimization and using them in the development of fundamental signal processing methods ranging from filtering to spectrum estimation, linear prediction, adaptive sampling and dimensionality reduction.

Course contents

Random varibles and vectors

Expectation

Moments and generating function

Covariance

Stochastic processes

Joint probability

Correlations and covariances

Projections

Static linear processing of random vectors

Quantization of random variables

Linear filtering of stochastic processes

z-transform

Structure and model for discrete-time linear filters

Stability

Design methods for discrete-time linear filters

Gaussian random vectors

Gaussian stochastic processes, white noise

Power spectrum

Wiener-Khinchin theorem

Elements of estimation theory

Periodogram spectral estimation

Modified-periodogram spectral estimation

Estimation of correlation

Minimum-variance spectral estimation

Linear prediction

Orthogonality principle

Yule-Walker equations

Finite-memory processes

Finite Markov chains

Office hours

See the website of Riccardo Rovatti

See the website of Mauro Mangia